Question

In non uniform circular motion, the ratio of radial acceleration to tangential acceleration is (V is the velocity, r is the radius and \(α\) is the angular acceleration)

• A. \(\frac{αr}{V}\)
• B. \(\frac{V^2}{r^2α}\)
• C. \(\frac{r^2α}{V^2}\)
• D. \(\frac{rα^2}{V^2}\)

Hint:

Radial acceleration is V^2/r and tangential acceleration is alpha times r.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In non-uniform circular motion the speed changes. The total acceleration has two parts: radial (centripetal) and tangential.

Step 2: Write the two components:
Radial acceleration \(a_r=\dfrac{V^2}{r}\). Tangential acceleration \(a_t=\alpha r\), where \(\alpha\) is the angular acceleration.

Step 3: Take the ratio:
\[ \dfrac{a_r}{a_t}=\dfrac{V^2/r}{\alpha r}=\dfrac{V^2}{r^2\alpha} \]
Option B.

Step 4: Why the other options are wrong.
Option A, \(\dfrac{\alpha r}{V}\), has the wrong dimension (it is not dimensionless). Option C is the inverse of the right ratio. Option D has the wrong powers of \(\alpha\) and \(r\).

Final Answer:
The ratio is V^2 / (r^2 alpha). \[ \boxed{\text{(B) }\dfrac{V^2}{r^2\alpha}} \]